ABS warp

I'm printing with ABS onto blue painter's tape. I don't have a heated bed, so I'm getting a fair bit of warp. However, the problem I have is not that the plastic lifts from the tape. Instead, the tape peels up from the MDF bed. I expect some warp using ABS without a heated bed, but I was under the impression that other people were using a similar set up with moderate success.

Can anyone either confirm using ABS on a non-heated bed, or perhaps point out what I'm doing wrong?

If the tape is lifting, you might try something nophead came up with. Admittedly he's having the issue with Kapton and a heated bed, but the same principle may help:

Some corners like it hot

Basically, by putting a small bead of plastic close to the edges of parts on the outside of the object, only a few layers high, it keeps pressure on the tape keeping it in place.

Another thing to check is that the bed is clean of solvent before you put the tape down. If you've used cleaning solvent and then put tape down on some of the residue, the glue on the tape will be affected. You want it clean, not only of old glue, but of residue from cleaning fluids.

Update: I switched from an MDF bed to an acrylic bed. Using the acrylic bed + "aprons" at the corners helped significantly.